1. Field of the Invention
The present invention relates to a surface shape measurement apparatus for measuring a shape of a surface to be measured.
2. Description of the Related Art
As a representative method of measuring a surface shape of a spherical lens or aspherical lens, a method of scanning by tracking a surface to be measured using a probe is known. As a typical method, a probe attached to a 3-axis orthogonal stage having X-, Y-, and Z-axis stages is scanned so that the distance between the probe and a surface to be measured becomes constant. By sequentially measuring the positions of the probe on this scanned surface using, for example, a laser distance measuring device, the shape of the surface to be measured can be obtained as a three-dimensional coordinate point group.
In the method of measuring the shape by scanning or tracking the surface to be measured using the probe, it becomes important to calibrate a coordinate system so as to guarantee high measurement precision. As a calibration method of the coordinate system, a method of comparing measured data obtained by measuring a reference surface (masterpiece) and reference data and minimizing their difference is generally used. Japanese Patent No. 3474448 discloses a method of calibrating a coordinate system using a reference spherical surface as a reference surface. With this method, using the fact that when the degree of orthogonality of the coordinate system is inaccurate, the spherical surface is measured as an elliptical surface, errors of the degrees of coordinates orthogonality of the coordinate system are calibrated so that the measured elliptical surface becomes a spherical surface.
In the method of calibrating the coordinate system using the reference surface, when a difference between the shape of the surface to be measured and that of the reference surface becomes large, the measurement precision lowers. This is because a moving region of the probe upon measuring the reference surface is different from that upon measuring the surface to be measured since the probe is used to contour-scan the surface to be measured. In general, the degrees of coordinates orthogonality between partial regions in a measurable region of a shape measuring device are different on an order of sub parts per million (ppm). For this reason, due to the different moving regions of the probe, a shape suffers shape errors on submicron to nanometer orders, which cannot be ignored in high-precision shape measurement.